Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 6x + 6$ and $ KL = 2x + 34$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {6x + 6} = {2x + 34}$ Solve for $x$ $ 4x = 28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 6({7}) + 6$ $ KL = 2({7}) + 34$ $ JK = 42 + 6$ $ KL = 14 + 34$ $ JK = 48$ $ KL = 48$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {48} + {48}$ $ JL = 96$